2018/07/16 by Paul Barry, Barry, Paul
Arts and Humanities · Mathematics · #11B37 #14H52 #15B05 #15B36 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Language, Linguistics, Cultural Analysis #Primary 11B83 #Secondary 11C20
paper · pdf · doi:10.48550/arxiv.1807.05794
openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a three parameter family of Bell pseudo-involutions in the Riordan group. The defining sequences have generating functions that are expressible as continued fractions. We indicate that the Hankel transforms of the defining sequences, and of the A sequences of the corresponding Riordan arrays, can be associated with Somos 4 sequence. We give examples where these sequences can be associated with elliptic curves, and we exhibit instances where elliptic curves can give rise to associated Riordan pseudo-involutions. In the case of a particular one parameter family of elliptic curves, we show how we can associate to each such curve a unique Bell pseudo-involution.